Electrofhfmico Acta, Vol. 38, No. Z/3, pp. 447-453, 1993 0013~4686/93 $6.00 + 0.00 zyxwvuts Printed in Gnat Britain. 0 1992 Pergamott Press Ltd EXERGY EFFICIENCY AND LOCAL HEAT PRODUCTION IN SOLID OXIDE FUEL CELLS SIGNE KJELSTRUP RATKJE* and STEFFEN MBLLER-HOLST Division of Physical Chemistry, Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim, Norway (Received 16 January 1992; in revisedform 27 April 1992) Ahstrati-The electric work method has been applied to a unit cell of the solid oxide fuel cell. A new equation for the cell power is derived, which takes into account temperature gradients of the system. Local heat productions and consumptions in the cell have been calculated using new data on the trans- ported entropy of oxygen ions. Exergy efficiency calculations are carried out for the unit cell at 1000°C indicating the relative importance of losses due to overpotentials, ohmic resistance and cracks in the electrolyte, incomplete reactions and temperature gradients. Energy economy is obtained for direct elec- trochemical conversion of methane in the unit cell when the overpotential at the fuel electrode is less than 0.21 V for an electric current density j = 1 Acm -‘. Ohmic resistance of the electrolyte plays a minor role. A natural temperature gradient of 10 K across the cell reduces the work from the cell by 0.6%. The heat production in the cell is asymmetrical. A 3% gain in exergy efllciency is obtained by changing the pres- sure from 1 to 4 bar. The results will have a bearing on cell design and material development. Key words: SOFC, fuel cell, exergy efliciency, electric work method, heat production. 1. INTRODUCI’ION Fuel cells are expected to play an important role in future production of electrical energy. The solid oxide fuel cell (SOFC) converts hydrogen and oxygen to water around 1000°C. Hydrogen may be produced outside or inside the cell before conver- sion. The success of the SOFC relative to other fuel cells or other power generating systems may depend on exploit of the heat production of the cell[l]. The heat production may be used for the reforming reac- tion which produces hydrogen[2] from natural gas, and for cogeneration of electricity[l]. Takehara and coworkers show that the heat production differs between electrodes in the SOFC unit cell[3]. They also discuss how the temperature distribution in the cell may vary in a tubular cell construction[4]. Rosen[l] concludes that exergy analyses should be used to evaluate efficiencies of power generating systems. We shall give the results of an exergy analysis of the SOFC, using a new method, the elec- tric work methodC5, 63. Our conclusion agrees on a general basis with that of Rosen[l], but more details of the process are given. The characteristics of the method are detailed descriptions of causes and loca- tion of local heat and energy changes per unit time. The analysis extends the work of Takehara and coworkers[3, 41 on this point, because the electric work method is more accurate than previously published methods. The analysis reveals the main factors for further improvement of the cell efficiency. The effect of the reformer reaction on the exergy efficiency will be quantified. Electrochemical conversion of methane will be compared with the process where hydrogen is * Author to whom correspondence should be addressed. externally produced from methane and further con- verted in the cell. A detailed discussion of the energy gain by cogeneration must, however, be postponed. We shall limit ourselves to the calculation of a unit cell. Unit cell descriptions are required for com- puter modelling of the system[7]. Both reversible and irreversible heat effects are taken into account, but losses due to diffusion will be neglected. 2. PRINCIPLES Assume that hydrogen for the fuel cell is supplied by reforming of methane according to the reaction: jCH,(g) + tH,O(g) --) jH,(g) + &O,(g). (r) Hydrogen is consumed inside the cell according to : #Mg) + 302-bd -, 3UW + e- (11) j02-(cat) + jO’-(an) (III) +0,(g) + e- + jot-(cat) (Iv) 9-W) + to,(g) -, fHzO@ 09 where (an) and (cat) refer to the anode and cathode, respectively. All reactions are written for the transfer of one faraday of elementary charges and the trans- ference number of O’- in the electrolyte is unity[8]. The overall reaction of the system is the sum of reac- tions (I) and (V); &H,(g) + to,(g) -+ tH,O(g) + @O,(g). (VI) We shall use the conversion ratios qcH4, )I”*, and ftol for reactions (I), (II) and (IV), respectively. EA 36-213-T 447